login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191554 a(n) = Product_{k=1..n} prime(k)^(2^(k-1)). 4
2, 18, 11250, 64854011250, 2980024297506569894680811250, 1319492964487055911863581348741902326769016593763234907139211250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

x^(2^n) - a(n) is the minimal polynomial over Q for the algebraic number sqrt(p(n)*sqrt(p(n-1)*...*sqrt(p(2)*sqrt(p(1)))...)), where p(k) is the k-th prime.  Each such monic polynomial is irreducible by Eisenstein's Criterion (using p = 2).

LINKS

Table of n, a(n) for n=1..6.

FORMULA

For n > 1, a(n) = a(n-1) * prime(n)^(2^(n-1)); a(1) = prime(1).

EXAMPLE

a(1) = 2^1 = 2 and x^2 - 2 is the minimal polynomial for the algebraic number sqrt(2).

a(4) = 2^1*3^2*5^4*7^8 = 64854011250 and x^16 - 64854011250 is the minimal polynomial for the algebraic number sqrt(7*sqrt(5*sqrt(3*sqrt(2)))).

PROG

(PARI) a(n) = prod(k=1, n, prime(k)^(2^(k-1)))

CROSSREFS

Cf. A191555.

Sequence in context: A309972 A208056 A276092 * A066361 A120929 A007184

Adjacent sequences:  A191551 A191552 A191553 * A191555 A191556 A191557

KEYWORD

nonn,easy

AUTHOR

Rick L. Shepherd, Jun 05 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)